Difference between revisions of "File:E1efig09abc1a150.png"
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| + | [[Complex map]]s of [[tetration]] $\mathrm{tet}_b$ to base<br> |
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| − | Importing image file |
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| + | $b\!=\!1.5$ , left, <br> |
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| + | $b\!=\!\exp(1/\mathrm e)$ , center, and<br> |
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| + | $b\!=\!\sqrt{2}$ , right. |
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| + | |||
| + | $f\!=\! \mathrm{tet}(x\!+\!\mathrm i y)$ is shown in the $x,y$ plane with levels |
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| + | $~p\!=\!\Re(f)\!=\! \mathrm{const}~$ and levels |
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| + | $~q\!=\!\Im(f)\!=\! \mathrm{const}~$. The integer levels are shown with thick lines. |
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| + | |||
| + | This image is close to the figure 9 in the article |
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| + | <ref name="e1e"> |
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| + | http://tori.ils.uec.ac.jp/PAPERS/2011e1e.pdf |
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| + | H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). (Mathematics of Computation, 2011, in press) |
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| + | </ref>. |
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| + | |||
| + | The [[C++]] generators of the pictures used in the figure are available and will be uploaded upon request. |
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| + | |||
| + | Copyleft 2011 by Dmitrii Kouznetsov. You may copy, modify and/or distribute the image for free but the source should be attributed. |
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| + | ==References== |
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| + | <references/> |
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| + | |||
| + | [[Category:Tetration]] |
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| + | [[Category:Complex maps]] |
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| + | [[Category:Holomorphic functions]] |
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Revision as of 09:39, 21 June 2013
Complex maps of tetration $\mathrm{tet}_b$ to base
$b\!=\!1.5$ , left,
$b\!=\!\exp(1/\mathrm e)$ , center, and
$b\!=\!\sqrt{2}$ , right.
$f\!=\! \mathrm{tet}(x\!+\!\mathrm i y)$ is shown in the $x,y$ plane with levels $~p\!=\!\Re(f)\!=\! \mathrm{const}~$ and levels $~q\!=\!\Im(f)\!=\! \mathrm{const}~$. The integer levels are shown with thick lines.
This image is close to the figure 9 in the article [1].
The C++ generators of the pictures used in the figure are available and will be uploaded upon request.
Copyleft 2011 by Dmitrii Kouznetsov. You may copy, modify and/or distribute the image for free but the source should be attributed.
References
- ↑ http://tori.ils.uec.ac.jp/PAPERS/2011e1e.pdf H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). (Mathematics of Computation, 2011, in press)
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